Question

Use this for the day before the day of your work

Answer 1

Answer:

Step-by-step explanation:

The given equation is:

`(1)/(2)mv^2+mgh=E`

Note that:

The mass m is constant

Total energy E is constant

The derivative of a constant is zero

g = 9.81 m/s^2

dh/dt = v

Compute d/dt of both sides

`\begin{gathered} (d)/(dt)((1)/(2)mv^2)+(d)/(dt)(mgh)=(dE)/(dt) \\ \\ (1)/(2)m(d)/(dt)(v^2)+mg(dh)/(dt)=0 \\ \\ (1)/(2)(m)(2v)(dv)/(dt)+mgv=0 \\ \\ mv(dv)/(dt)+mgv=0 \\ \\ mv(dv)/(dt)+9.81mv=0 \\ \\ mv((dv)/(dt)+9.81)=0 \\ \\ (dv)/(dt)+9.81=0 \\ \\ (dv)/(dt)=-9.81\text{ m/s}^2 \end{gathered}`